CODEWITHSUNDEEP
c++mathfloating-point
May Oakes
May Oakes

Reputation: 4619

Floating point operations resulting in a number that is essentially zero

I'm doing some calculations that result in a value like {-0.707107, 9.61481e-017, 0.707107} when I'm expecting {-0.707107, 0, 0.707107}. Could that second component, while essentially zero, cause problems down the road? Should I do something about it? Using C++ doubles.

Upvotes: 1

Views: 305

Answers (4)

Stephen Canon
Stephen Canon

Reputation: 106117

They will only "cause problems" if you (a) are doing a numerically unstable calculation (you probably aren't) or (b) will later attempt to compare them using strict equality. In general, you shouldn't "do something" about it, you should just make sure that your algorithm is not overly sensitive to a small amount of imprecision.

Upvotes: 5

Martin Beckett
Martin Beckett

Reputation: 96119

You can only safely use == for comparing floats for certain values and even then only when you have assigned those values directly, you can't use it for the result of any calcualtion.

normally you define a function 

bool isEqual(double a,double b) {
  return fabs(a-b) < 0.0000001; // depends on the precision of your application
}

bool isClose(double a,double b) {
  return fabs(a-b) < 0.001;
}

Upvotes: 1

Aasmund Eldhuset
Aasmund Eldhuset

Reputation: 37940

That depends very much on what you intend to do down the road. :-) However, getting results that are very close to, but not exactly equal, to what the "mathematical" result should be, is something one must live with when using floating point numbers. A common solution is to define some "epsilon" value (say, 1e-10) and accept an error of epsilon in all comparisons - so x == y would become fabs(x - y) < epsilon.

Upvotes: 6

Fred Foo
Fred Foo

Reputation: 363467

Yes they could cause problems, when comparing with 0. using ==: that will return false. Such rounding errors may also accumulate, as @driis noted.

What you can do about this: instead of comparing using ==, use a comparison that allows for round-off errors, and/or discard values that are below a reasonable threshold at appropriate points in the algorithm, depending on what you want to do with the values.

See any good book on numerical algorithms.

Upvotes: 1

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